Question
$$10\cdot\frac{1}{3}-4\cdot\frac{5}{6} = 0$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 10\cdot\frac{1}{3}-4\cdot\frac{5}{6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot10\cdot\frac{1}{3}-6\cdot4\cdot\frac{5}{6} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]20-20 &= 0&& \text{simplify left side} \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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